Problem 9.10

กำหนดให้ \(L = 2.00 m, A = 0.0500\times 10^{-4} m^{2}, Y = 2.00\times 10^{11} N/m^{2},\)

\(m = 1,000 kg, u = 0 m/s, s = 10.0 m, t = 2.00 s\)

และ \(g = 9.80 m/s^{2}\)

จาก \(Σ\vec{F} = m\vec{a}\)

\(F - mg = m(\frac{2(s - ut)}{t^{2}});\vec{s}=\vec{u}t+\frac{1}{2}\vec{a}t^{2}\)

\(σA - mg =\frac{2ms}{t^{2}};σ=\frac{F}{A},u=0m/s\)

\(YεA - mg =\frac{2ms}{t^{2}}; Y =\frac{σ}{ε}\)

\(Y(\frac{\Delta L}{L})A - mg =\frac{2ms}{t^{2}}; ε =\frac{\Delta L}{L}\)

\(\Delta L =\frac{mL}{AY}(g +\frac{2s}{t^{2}})\)

\(\Delta L = 2.96 cm \;\blacksquare\)